Question

Express (Cosx + i sinx / sin x + i cos x) in the form of Cos A + i sin A.
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Answer 1

Answer:

Step-by-step explanation:

$\implies \sf{\dfrac{cosx + isinx}{sinx+icosx}}\\\\\\\implies\sf{\dfrac{cosx+isinx}{sinx+icosx}\times \dfrac{sinx - icosx}{sinx - icosx}}\\\\\\\implies \sf{\dfrac{(cosx + isinx)(sinx-icosx)}{(sinx + icosx)(sinx -icosx)} }\\\\\\\implies \sf{\dfrac{cosx.sinx - icos^2x + isin^2x - i^2 sinx.cosx}{sin^2x - i^2.cos^2x }}\\\\\\\implies \sf{\dfrac{cosx.sinx + i(sin^2x - cos^2x) +sinx.cosx}{sinx^2x + cos^2x}}\\\\\\\implies \sf{\dfrac{2sinx.cosx + i(cos2x)}{1}}\\\\\implies \sf{sin2x + icos2x}$

$\implies \sf{cos(\frac{\pi}{2}-2x) + isin(\frac{\pi}{2} - 2x)}$

Answer 2

For further Explanation

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